the author changes his mind about the sub-category chosen
I'd say definite no for this condition. Better to click the "Report to moderator" link and request the thread be moved to the other category. Of course we should try our best to get it right the first time because I'm sure the moderators already have plenty of work to do but if they're just going to have to merge the two posts anyway (and who knows whether it will be merged to the category you like).
(no response is received for a post
&& the subject is in gray areas regarding sub-categories)
What is allowed (but maybe not encouraged) is to bump your post "after a couple days", as stated in the rules:
I think it's best to add information to the bump if possible, such as what you've tried over the couple days, rather than just a no-content bump.
As for the crossposting question, I'm can't give an authoritative answer but IF it is allowed it's very important to add a link to the other post and edit the original post to add a link to the new post. That way people can check the other thread to see if it's been answered or if there is more information there. I'd also like to see people do that when posting the same question to multiple sites. Apparently a significant number of the regulars here think it is OK to post the same question to multiple sites but it really ticks me off when I spend a bunch of time on a question here only to browse over to Stack Exchange or the GitHub issue tracker after and find out that someone else had already posted the same response as me earlier.